A cylinder has a base area of [tex]169\pi \, \text{ft}^2[/tex] and a height that is twice the radius. What is the lateral area and surface area of the cylinder?

A re a o f ba se : A B ​ = 169 π f t 2 A B ​ = π r 2 ( r − r a d i u s ) π r 2 = 169 π / : π r 2 = 169 r = 169 ​ r = 13 ( f t ) H = 2 r → H = 2 ⋅ 13 = 26 ( f t )
l a t er a l a re a : A L ​ = 2 π rH A L ​ = 2 π ⋅ 13 ⋅ 26 = 676 π ( f t 2 ) S u r f a ce a re a : A S ​ = 2 A B ​ + A L ​ A S ​ = 2 ⋅ 169 π + 676 π = 338 π + 676 π = 1014 π ( f t 2 )

Answered by Anonymous | 2024-06-10

Area of base = 169 π
r = √Area = 13 ft
Given, height = 2 x 13 = 26 ft.
Lateral surface area of cylinder = 2πrh = 2 x π x 13 x 26 = 676 π ft²
Total surface area = 2πr(r + h) = 2 x π x 13 x 39 = 1014 π ft²
Thus, lateral surface area is 676 ft² and total surface area is 1014 ft²

Answered by tadvisohil886 | 2024-06-10

The lateral area of the cylinder is 676 π ft 2 and the total surface area is 1014 π ft 2 . The calculations begin with finding the radius from the given base area, which leads to the height being determined as double the radius. Finally, both the lateral area and the surface area are calculated using relevant formulas.
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Answered by Anonymous | 2024-12-23